588 Achilles is an asteroid discovered on February 22, 1906 by the German astronomer Max Wolf. It was the first of the Trojan asteroids to be discovered, and is named after Achilles, a fictional hero from the Trojan War. It orbits in the L4 Lagrangian point of the Sun-Jupiter system. After a few such asteroids were discovered, the rule was established that the L4 point was the "Greek camp", while the L5 point was the "Trojan camp", though not before each camp had acquired a "spy" (624 Hektor in the Greek camp and 617 Patroclus in the Trojan camp).